An analytical study has been conducted for natural convection in a cavity of different aspect ratios with uniform volumetric heat generation. Two different boundary conditions are investigated for the cavity, viz., all walls are isothermal; two horizontal walls are adiabatic and two vertical walls are isothermal. A stream function vorticity formulation is used where the variables are expanded in terms of Rayleigh number, defined as Ra=g{sup}βh{sup}5q{sup}(III)/αvk. The governing equations are reduced, to biharmonic equations, and these biharmonic equations are solved using one of the methods, available in the literature. It is observed that the horizontal component of velocity is smaller than the vertical component near the center and the vertical walls of the cavity. The results for velocity profiles are compared with the simulations obtained from Fluent and they are found to be in good agreement.
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机译：已经对具有不同长径比的腔体中自然对流进行了分析研究，并产生了均匀的体积热量。研究了空腔的两种不同边界条件，即所有壁都是等温的。两个水平壁是绝热的，两个垂直壁是等温的。使用流函数涡度公式，其中变量根据瑞利数扩展，定义为Ra = g {sup}βh{sup} 5q {sup}（III）/αvk。控制方程简化为双调和方程，这些双调和方程使用文献中提供的一种方法求解。可以看出，速度的水平分量小于空腔中心和垂直壁附近的垂直分量。将速度分布图的结果与从Fluent获得的仿真结果进行比较，发现它们具有很好的一致性。
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